S. Remmler, M.D. Fruman, S. Hickel (2013)
Journal of Fluid Mechanics 722: 424-436. doi: 10.1017/jfm.2013.108

We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an- plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere.

We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.


Left: Computational domain in the rotated coordinate system x,y,z. The earth coordinates are denoted as x',y',z'. cp and cg indicate the phase and group velocity. Right: Initial condition with secondary singular vector perturbation. Contours of buoyancy in red and blue, and an iso-surface at b = 0 showing the initial perturbation in green.

Temporal evolution of the first three breaking events. Background: plane at y = 400m coloured by buoyancy; foreground: iso-surface of Q = 0.004s−2, indicating turbulent vortices.


Time series for the non-dimensional amplitude of the primary wave and total energy dissipation for different secondary perturbations and domain sizes.